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A friendly introduction to the Friendship Paradox (2021)
- notenoughbeans 4y agoIf my friends have more friends than me, do their friends have more friends than them? And if I'm my friend's friend, am I not included in their friends that have more friends?
- lupire 4y agoNo, because the statement is about averages (normal people), not the outliers (celebrities) that average people are friends with.
- tshaddox 4y agoCelebrities are a much less counterintuitive example. The effect is quite obvious if you look at asymmetric relations like being aware of a famous person (or, say, Twitter follows). It's pretty obvious that a lot more people know Justin Bieber or Barack Obama by name than the pop star or U.S. President know by name. What's slightly less intuitive about the friendship paradox is that this also tends to be true with symmetric relations.
- vikingerik 4y agoThe real title and the principle are "your friends more likely have more friends than you". It's not true in every case, and obviously not on both sides of a reciprocal pair.
- taneq 4y agoExactly. The heavy lifting in this case is being done by the phrase “on average.” They could have just said “a small number of people have WAY more friends than usual.”
- tshaddox 4y ago> They could have just said “a small number of people have WAY more friends than usual.” They do say that, but that's a way to explain why the friendship paradox is true. It's not some trivially equivalent statement. If the statements were trivially equivalent, then people wouldn't be complaining that one is counterintuitive while the other is obvious. The whole point is that one fact is a counterintuitive result of another more intuitive fact.
- micah94 4y agoWhenever you start talking about averages, you have to be careful. The average nuclear family having 2.5 kids, for example.
- Oxidation 4y agoMore like 2.499 once you consider the mass defect when you fission the third child.
- aidenn0 4y agoIf you select a random person, and then select a random friend of that person, most of the time, the latter has more friends. This is because friendship graphs tend to have a small number of highly-connected nodes and a large number of less-connected nodes. Therefore most of the connections are between a less-connected node and a more connected node. So, if you just select a random node, you are highly likely to select a less-connected node, which also means that if you follow a random connection from that node, you are likely to reach a highly connected node. So to answer your original question: No.
- triyambakam 4y agoThanks for the succinct summary, I understand it better than the featured article.
- taeric 4y agoThat summary is still confusing to me. Rather, "If you select a random person, and then average how many friends all of their friends have, most of the time the latter will be higher." I don't think it holds nearly as strongly in the case of selecting a single neighbor. (I can't say it doesn't hold.)
- aidenn0 4y agoLet's simplify this a bit. Divide people into "lots of friends" (L) and "few friends" (F). Most nodes are F, most edges are F<->L. Therefore if you randomly select a person, you probably end up with an F. Since most edges are F<->L, following an edge from an F is likely to get you to an L.
- taeric 4y agoI could see a plurality of edges are actually F<->F, though? Such that most people you connect with are connected with everyone else you also connect with. You will just have a few people in any large group that are hyper connected outside of that group. Such that, as likely, you have the same number of friends as any given friend. Similarly, though, most likely you will have fewer friends than the average of all of your friends.
- tshaddox 4y agoWell, no, it doesn't work like that. There's already not some guarantee that your friends will have more friends than you do. Obviously some of the people have to be the ones that have lots of friends, and you could very well be one of those people. The point is just that most people aren't those people, so most people who read these articles and check their friend graphs will go "whoa, it's true!"
- adammarples 4y agoNo their friend's friends do not have more friends than them. Some people have an unusually large amount of friends, what this means practically is that they are more likely to be one of your very few friends, because they touch so many smaller groups, yours included. When they say most people's friends have more friends than them, it's the same very popular people being counted again and again by each unpopular person.
- lupire 4y agoThis is the Friendship Paradox of graph theory: https://en.wikipedia.org/wiki/Friendship_paradox https://en.wikipedia.org/wiki/Friendship_paradox
- xapata 4y agoMedian is sometimes more relevant than mean.
- romwell 4y agoAs a mathematician, my immediate reaction was: duh! Of course! Why is this interesting? The go-to example would be a person having 10 friends, being the only friend for each of them. It's not too hard to generalize from there, or at least to have an intuition. The interesting part for me was this: > If there are only enough vaccines for a small fraction of the population, an effective strategy is to vaccinate a random friend of each randomly chosen person. Oh. Makes sense! Somehow, something like that didn't occur to me even when the math felt intuitive.
- mkehrt 4y agoWell, the interesting thing isn't that such graphs exist, so finding an arbitrary graph with this property isn't really relevant. It's that certain distributions of random graphs, when sampled tend to produce graphs with this property and human social networks are one of them.
- romwell 4y agoTrue. My comment was to highlight how wrong my initial intuition was. Looking around, this article[1] by Arun Maiya and Tanya Berger-Wolf explores this in the context of social networks. Fascinating stuff! [1] https://arxiv.org/pdf/1109.3911.pdf https://arxiv.org/pdf/1109.3911.pdf
- woopwoop 4y agoNo, this statement is true for every graph that doesn't have constant degree. It's not really to do with random graphs. Rather it's the fact that a random neighbor of a random node draws from a different distribution than a random node, and the former distribution puts more mass on nodes of higher degree.
- mkehrt 4y agoAh, oops, you are correct.
- kinban123 4y agoDoes this logic extend? What if i reached out to a random friend of a random friend of a random node - basically to degree 3 of the network. Is that better than degree 2 ? If so, then is there a degree where the spreading is optimal ?
- woah 4y agoOn the bright side, the people you are not friends with have fewer friends than you do.
- deleted 4y ago[deleted]
- smeej 4y agoThis answer made me laugh so much harder than it should have. I'm thanking the art of selective statistics for this little highlight in my day!
- sitkack 4y agoHow to Lie with Statistics by Darrel Huff is really good satire https://archive.org/details/HowToLieWithStatistics_201608 https://archive.org/details/HowToLieWithStatistics_201608 From page 32 in the chapter on how to "choose the right average" > You and your partners have paid yourselves $11,000 each in salaries. You find there are profits for the year of $45,000 to be divided equally among you. How are you going to describe this? To make it easy to understand, you put it in the form of averages. Since all the employees are doing about the same kind of work for similar pay, it won’t make much difference whether you use a mean or a median. > This is what you come out with: > Average wage of employees $ 2,200 > Average salary and profit of owners .... 26,000 > That looks terrible, doesn’t it? Let’s try it another way > Take $30,000 of the profits and distribute it among the three partners as bonuses. And this time when you aver- age up the wages, include yourself and your partners. And be sure to use a mean.
- CalChris 4y agoCousins also have cousins that aren't related to you.
- dismantlethesun 4y agoBut that one is kind of trivial. Your cousins have parents who aren't related to you. Colloquially speaking, people have 'uncles' and 'aunts' that they share no blood with.
- tshaddox 4y agoIndeed. An interesting exercise might be to ask yourself if the friendship paradox applies to cousin relationships (let's limit it to first cousins with zero removal).
- ljf 4y agoThe one that throws me is: If you are a parent (say a father), and DO NOT have a child of the same sex as you (a son in this case), you have broken an unbroken line of parents before you who had a child of the same sex. Every father that came before you had at least one son that lived to have their own children, and had a son... It's simple but blows my tiny mind. My mother was quite shocked when she learnt the female line broke with her. :P
- jacooper 4y ago404?
- chris_wot 4y agoSame.
- dpkirchner 4y agoTry reloading a few times. Guessing one of their backends doesn't have the files yet.
- romwell 4y ago'tis the Slashdot hug effect. Pardon, HN DDOS. Mirrors: [1] https://archive.ph/nzKWP https://archive.ph/nzKWP [2] https://web.archive.org/web/20221128230655/https://scribe.citizen4.eu/your-friends-have-more-friends-than-you-e005796841bb https://web.archive.org/web/20221128230655/https://scribe.ci...
- phkahler 4y agoOn a sort of related note, men and women have the same average number of sexual partners. Assuming equal numbers of each in the population and only considering heterosexual sex. Edit: if we consider TFA do our partners have more partners than us on average?
- antisthenes 4y agoThe average human has 1 testicle and 1 ovary. On a sort of related note.
- nostromo 4y agoThe average human also has less than two legs.
- pessimizer 4y agoErasure of the third leg community.
- FeistySkink 4y agoThird leg - every photographer's dream.
- Manuel_D 4y agoMean and median are two different things. By definition, mean heterosexual partners are exactly identical but median can vary between men and women.
- fergie 4y agoYes, but according to the Friendship Paradox _your_ sexual partners are likely to have had more sexual partners than you.
- christiangenco 4y agoOh—I think this is just another Pareto distribution: a small minority of people have the majority of friends (probably something like the top 20% of people have 80% of the friends). You're probably friends with several people in that top 20% because they know a lot of people. The average number of friends your friends have including the outliers is going to be higher than the number of friends you have.
- xypage 4y agoI don't think that's a good representation of what they're saying. They showed that the average number of friends that your friends will have is mu+std/mu, so if the distribution is anything but perfectly homogeneous then you can expect that your friends will have more friends than you. It doesn't need to be super skewed with some people knowing everybody, any variation _at all_ leads to this, no need for outliers.
- pessimizer 4y ago> any variation _at all_ leads to this, no need for outliers. A lot of dismissals miss this in talk about super popular celebrities. It just requires that some people have more friends than other people. The people who have more friends are more likely to be friends with you than the people who have fewer friends [edit: even if "more friends" means five friends and "fewer friends" means four friends.] That's it. It isn't about outliers pulling up means.
- WastingMyTime89 4y agoTheir description seems like a fairly good take. The main idea is that in graph you are more likely to be connected to an outlier when it comes to connexions by virtue of them being more connected and these outliers skew the average. Of course you might yourself be the outlier. If you think about it, this is not far from saying that: if you know a distribution is non homogenous with a limited number of elements skewed - like say a normal distribution - and pick an element at random, it is more likely to be average than exceptional which is pretty trivial when you think about it.
- zeroimpl 4y agoHow would the results differ if you looked at median instead of average? It seems like median would probably be about the same in many cases, when talking about # of friends.
- fnordpiglet 4y agoThis is why I intentionally make close friends.
- tacitusarc 4y agoThis is a good example of why the mean is often unhelpful.
- jsnell 4y agoNeither of the epidemiology examples makes any sense to me. There seems to be some kind of implicit assumption that people with more friends are more likely to be infected, but that really isn't how friendship works.
- alchemist1e9 4y agoWhat if the two people don’t agree they are friends? For some reason I know a lot of people who think they are my friend and claim as such but in my mind they aren’t and I know they tend to talk to me in their self interest.
- marius_k 4y agoThat is why I choose to have zero friends.
- fjfaase 4y agoJust as counter intuitive as that all file compression methods make most of all possible files larger.
- deleted 4y ago[deleted]